Question

A normal population has mean μ = 9 and standard deviation σ = 6.

a.	What proportion of the population is less than 20?
b.	What is the probability that a randomly chosen value will be greater than 5?

Answer 1

Solution :

Given that ,

mean = = 9

standard deviation = = 6

a.

P(x < 20) = P[(x - ) / < (20 - 9) / 6]

= P(z < 1.83)

= 0.9664

proportion = 0.9664

b.

P(x > 5) = 1 - P(x < 5)

= 1 - P[(x - ) / < (5 - 9) / 6)

= 1 - P(z < -0.67)

= 1 - 0.2514

= 0.7486

Probability = 0.7486